Final Presentation
報告人：賴尹天 許沛萱 吳卓鋮
Date：2019-01-11
配對交易 Pair Trading
如何操作
如果兩個相關性較高的股票或者其他證券之間出現背離，就應該買進表現相對較差的，賣出表現相對較好的。當未來兩者之間的背離得到糾正，那麼可以進行相反的平倉操作來獲取利潤。其本質上是一個反轉投資策略。
配對交易缺點
雖然該策略沒有太大的下行風險，但機會匱乏，而且，為了獲利，交易者必須是最先利用機會的人之一。其他一些風險包括：
• 市場風險的衡量標準，例如beta，是歷史性的，未來可能會比過去更加不同。 • 如果實施均值回歸策略，那麼假設未來的均值將與過去一樣保持不變。
配對交易步驟
Step 1：抓資料(2014年~2018年)及清理
# data = read.csv("C:/Users/amyhs/Desktop/碩士課程/時間序列/報告/期末報告/塑化類股.csv" , header = FALSE , sep = ",")
# codes = unlist(as.character(data[,1]))
#
# start = "2014-01-01"
# end = "2018-12-31"
#
# df.stock = getSymbols(codes[1] , src = 'yahoo' , auto.assign = FALSE , from = start , to = end)
# df.stock = Ad(df.stock)
#
#
# for (code in codes[2 : length(codes)]){
# stocks = getSymbols(code , src = 'yahoo' , auto.assign = FALSE , from = start , to = end)
# df.stock = cbind(df.stock , Ad(stocks))
# }
#
# colnames(df.stock) = codes
#
# save(df.stock , file = 'C:/Users/amyhs/Desktop/碩士課程/時間序列/報告/期末報告/塑化類股.RData')
load('C:/Users/amyhs/Desktop/碩士課程/時間序列/報告/期末報告/塑化類股.RData')
df = na.omit(df.stock)
# 將欄位名稱加x
colnames(df) = sapply(1:length(colnames(df)) , function(x)
{ colnames(df)[1] = str_c('x', str_sub(colnames(df[,x]),1,4)) })
# 取2014~2017
df_history = df['2014/2017',]Step 2：對股價做單根檢定
找出股價不穩定的個股 1. 此次adf檢定的套件選用tseries，該套件的adf檢定默認落後期數為trunc((length(x)-1)^(1/3))，trunc代表整數部分。 2. 此次報告所選2014-2017的股價數據共有979筆，因此默認落後期數為9.而fUnitRoots套件中的adf檢定落後期數默認為1. 3. 考慮到落後期數不同，檢定結果會有較大差異，因此我們每次做檢定都分別考慮（lag=1 3 5 7 9）五種情況，選取最小pvalue。
alpha = 0.05
# 取股價adf test p-value>0.05
adf = function(x){
pvalue = vector("numeric",5)
for (i in seq(1,9,2)){
temp = adf.test(x,k=i)[['p.value']]
pvalue[(i+1)/2] = temp
}
return(min(pvalue))
}
df_history = df_history[ , sapply(df_history, function(x) { adf(x) >= alpha })]
num = length(colnames(df_history))Step 3：兩兩建迴歸取出殘差
k = 1
for (i in seq(num)){
for (j in seq(num)){
risidual = lm(df_history[,i]~df_history[,j])[["residuals"]]
df_history = merge(df_history, risidual)
colnames(df_history)[num+k] = str_c(colnames(df_history[,i]),colnames(df_history[,j]))
k = k+1
}
}
# 把自己和自己的殘差刪除
for (i in seq(num)){
df_history[,((num+1)*i)] = NA
}
# 去除全部為NA的欄
df_history = df_history[, colSums(is.na(df_history)) != nrow(df_history)]Step 4：將殘差做單根檢定
找出最穩定的殘差
# 計算RESIDUAL P-VALUE
risidual_p = sapply((num+1):length(colnames(df_history)),
function(x){ adf(df_history[,x]) })
# 找P-VALUE最小的
risidual_min = df_history[ , which.min(risidual_p)+num]
name1 = str_sub(colnames(risidual_min),1,5)
name2 = str_sub(colnames(risidual_min),6,10)
name1## [1] "x1301"name2## [1] "x1304"取出歷史資料
stock1_history = df_history[,name1]
stock2_history = df_history[,name2]殘差圖形
plot(risidual_min , main = 'residual')
兩股票趨勢(2014~2017)
2014~2017
database1 = as.data.frame(df_history)
p = plot_ly(data = database1 , x = index(df_history)) %>%
add_lines(y = database1[,name1] , type = "scatter" , mode = "lines" ,
line = list(color = 'gray') , name = sprintf('%s.TW',name1)) %>%
add_lines(y = database1[,name2],
type = "scatter" , mode = "lines",
line = list(color = '#28B0FE') ,
yaxis = "y2", name = sprintf('%s.TW',name2)) %>%
layout(title = sprintf('%s.TW vs %s.TW' , name1 , name2),
xaxis = list(
rangeselector = list(
buttons = list(
list(
count = 3,
label = "3m",
step = "month",
stepmode = "backward"),
list(
count = 6,
label = "6m",
step = "month",
stepmode = "backward"),
list(
count = 1,
label = "1y",
step = "year",
stepmode = "backward"),
list(
count = 3,
label = "3y",
step = "year",
stepmode = "backward"),
list(
count = 5,
label = "5y",
step = "year",
stepmode = "backward"),
list(step = "all"))),
rangeslider = list(type = "date")),
yaxis = list(side = 'left' ,
title = sprintf('%s.TW',name1)) ,
yaxis2 = list(title = sprintf('%s.TW',name2) ,
overlaying = "y", side = "right"))
offline( p )取出2018資料
df_2018 = df['2018',]
stock1 = df_2018[,name1]
stock2 = df_2018[,name2]2018
df_2018 = df['2018',]
database2 = as.data.frame(df_2018)
p_2018 = plot_ly(data = database2 , x = index(df_2018)) %>%
add_lines(y = database2[,name1] , type = "scatter" , mode = "lines" ,
line = list(color = 'gray') , name = sprintf('%s.TW',name1)) %>%
add_lines(y = database2[,name2],
type = "scatter" , mode = "lines",
line = list(color = '#28B0FE') ,
yaxis = "y2", name = sprintf('%s.TW',name2)) %>%
layout(title = sprintf('%s.TW vs %s.TW' , name1 , name2),
xaxis = list(
rangeselector = list(
buttons = list(
list(
count = 3,
label = "3m",
step = "month",
stepmode = "backward"),
list(
count = 6,
label = "6m",
step = "month",
stepmode = "backward"),
list(
count = 1,
label = "1y",
step = "year",
stepmode = "backward"),
list(
count = 3,
label = "3y",
step = "year",
stepmode = "backward"),
list(
count = 5,
label = "5y",
step = "year",
stepmode = "backward"),
list(step = "all"))),
rangeslider = list(type = "date")),
yaxis = list(side = 'left' ,
title = sprintf('%s.TW',name1)) ,
yaxis2 = list(title = sprintf('%s.TW',name2) ,
overlaying = "y", side = "right"))
offline( p_2018 )交易策略
利用迴歸殘差最穩定的兩標的做配對交易
計算歷史截距項及beta
intercept = lm(stock1_history ~ stock2_history)[['coefficients']][[1]]
beta = lm(stock1_history ~ stock2_history)[['coefficients']][[2]]
beta_2018 = lm(stock1 ~ stock2)[['coefficients']][[2]]畫出歷史價差圖形
spread = stock1-stock2*beta-intercept
plot(spread, main='spread')
畫出2018價差圖形
spread_history = stock1_history - stock2_history*beta - intercept
plot(spread_history, main='spread')
將價差標準化
zscore = (spread-mean(spread_history))/sd(spread_history)
colnames(zscore) = 'zscore'
plot(zscore, main='zscore')
建立投資策略
| z-score | 交易訊號 |
|---|---|
| > 1.28 | 放空 |
| -0.25~0.25 | 平倉 |
| < 1.28 | 買進 |
portfolio = as.data.frame(cbind(zscore, stock1, stock2))
portfolio$return1 = ROC(portfolio[,name1], type = "continuous")
portfolio$return2 = ROC(portfolio[,name2], type = "continuous")
portfolio$position = NA
portfolio[1,"position"] = 0
portfolio$return = NA
# 大於1.28漲太多=>賣出
for (i in seq(length(zscore))){
if (portfolio[i,"zscore"] > 1.28){
portfolio[i,"position"] = -1
}
else if (portfolio[i,1]< -1.28){
portfolio[i,"position"] = 1
}
else if (abs(portfolio[i,1])< 0.25){
portfolio[i,"position"] = 0
}
}
head(portfolio)## zscore x1301 x1304 return1 return2 position
## 2018-01-02 1.959546 93.10741 15.82419 NA NA -1
## 2018-01-03 2.042126 93.48705 15.63236 0.004069140 -0.012196532 -1
## 2018-01-04 2.021458 93.48705 15.72822 0.000000000 0.006113745 -1
## 2018-01-05 2.000797 93.39214 15.77625 -0.001015736 0.003049156 -1
## 2018-01-08 2.103826 94.43617 15.82419 0.011116884 0.003033631 -1
## 2018-01-09 2.402664 97.28348 15.87212 0.029705138 0.003024519 -1
## return
## 2018-01-02 NA
## 2018-01-03 NA
## 2018-01-04 NA
## 2018-01-05 NA
## 2018-01-08 NA
## 2018-01-09 NA用fill函數將持有部位放入
portfolio = portfolio %>% fill(position,.direction = "down")計算報酬
portfolio$return = (portfolio$return1-beta*portfolio$return2)*portfolio$position交易結果
portfolio = na.omit(portfolio)
#計算累計報酬
portfolio$cumsum_re = NA
portfolio$cumsum_re = sapply(1:length(portfolio$cumsum_re),
function(x){ portfolio[x,"cumsum_re"]=exp(sum(portfolio[1:x,"return"])) })
plot(portfolio$cumsum_re, type='l', main='cumsum return')